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  • Author: Hery Randriamaro x
  • Mathematics x
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Abstract

The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and creation operators obey the quon algebra which interpolates between fermions and bosons. In this paper we generalize these models by introducing a deformation of the quon algebra generated by a collection of operators a i,k, (i, k) ∈ ℕ* × [m], on an infinite dimensional vector space satisfying the deformed q-mutator relations aj,lai,k=qai,kaj,l+qβk,lδi,j We prove the realizability of our model by showing that, for suitable values of q, the vector space generated by the particle states obtained by applying combinations of a i,k’s and ai,k ‘s to a vacuum state |0〉 is a Hilbert space. The proof particularly needs the investigation of the new statistic cinv and representations of the colored permutation group.